Opportunistic Angle of Arrival Estimation in Impaired Scenarios

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UNIVERSITÀ DEGLI STUDI DI UDINE

Dipartimento di Ingegneria Elettrica, Gestionale e Meccanica

Corso di Dottorato in Ingegneria Industriale e dell’Informazione

Ciclo XXIX

Tesi di Dottorato di Ricerca

OPPORTUNISTIC ANGLE OF ARRIVAL

ESTIMATION IN IMPAIRED SCENARIOS

Dottorando:

ANDREA PAPAIZ

Relatore:

Prof. ANDREA M. TONELLO

ANNO ACCADEMICO

2016/2017

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To <insert your name>,

for your outstanding <insert your quality>.

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Ringraziamenti

L’esperienza vissuta in questi tre anni di dottorato è stata molte cose: gratificante, sti-molante, divertente ma anche molto difficile e non di rado frustrante. Indipendentemente dalla situazione sono stato sempre e comunque debitamente supportato, sopportato e al-l’occorrenza insultato dagli efficientissimi e professionalissimi membri del WiPLi Lab, a pochi noto sotto lo pseudonimo di Ledraside Lab. Il WiPLi Lab, gruppo di cui sono stato un orgoglioso membro, è un piccolo e ben assortito clan di ingegneri creativi, dotati di pirotecnici cervelli e menti acute e curiose. Di seguito, in ordine di anzianità, qualche parola per ringraziarvi uno per uno. Fabio, inarrivabile esempio di efficienza accade-mica e pessimo autista, grazie delle preziose riflessioni. Marco, orgoglioso “hardwarista anonimo” con i piedi per terra e la mente tra le giganti rosse, grazie per la plètora di fondamentali consulenze e la pazienza. Mauro, profondo conoscitore dei labirinti della notazione matematica e delle segrete tracce tra i mughi, grazie per le rigorose risposte alle mie poco rigorose domande. Alberto, appassionato ballerino cesellatore di passi e di articoli scientifici, il bug-finder per eccellenza, grazie per l’incessante e asfissiante opera di review.

Inutile dire che la cosa che più mi mancherà di questa esperienza saranno i tanto appassionati quanto improvvisi brainstorming sugli argomenti più disparati, dai famosi “g-con-i” alla meteorologia, dall’astrofisica al concetto di colore.

Grazie e tutti e lunga vita al nostro WiPLi Lab!

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List of Figures

2.1 AoA estimation array system. . . 8

2.2 Arrays for AoA estimation. L array (left). X array (right). . . 12

2.3 FPA receiving scheme, Na= 2. . . 15

2.4 PPA receiving scheme, Na = 2. . . 16

2.5 TSA receiving scheme, Na = 2. . . 16

2.6 Example of Bi-dimensional (2D) angular uncertainty surfaces B generated by the same Mono-dimensional (1D) angular uncertainties δφ = δθ = 20◦ and leading different Ω values. . . 18

3.1 zero intermediate frequency (zero-IF) transmitter. . . 20

3.2 zero-IF receiver. . . 20

3.3 Received 16−QAM signal pdfs, ideal case. (a) Cartesian Complex - pdf (C-CP). (b) Polar Complex - pdf (P-CP). . . 22

3.4 Received 8-4-Amplitude Phase Shift Keying (PSK) (A-PSK) signal pdfs, ideal case. (a) C-CP. (b) P-CP. . . 23

3.5 Received 16-QAM signal pdfs showing DCO effects. (a) C-CP. (b) P-CP. . 25

3.6 Received 12-4-A-PSK signal pdfs showing DCO effects. (a) C-CP. (b) P-CP. 25 3.7 Received 16-QAM signal pdfs showing IQU effects. (a) C-CP. (b) P-CP. . 27

3.8 Received 8-4-A-PSK signal pdfs showing IQU effects. (a) C-CP. (b) P-CP. 28 3.9 Received 16-QAM signal pdfs showing IQS effects. (a) C-CP. (b) P-CP. . 29

3.10 Received 8-4-A-PSK signal pdfs showing IQS effects. (a) C-CP. (b) P-CP. 30 3.11 Received 16-QAM signal pdfs showing PO effects. (a) C-CP. (b) P-CP. . . 31

3.12 Received 8-4-A-PSK signal pdfs showing PO effects. (a) C-CP. (b) P-CP. . 32

4.1 CIR of a signal emitted by transmitter antenna and received in the center of the receiving array. . . 35

4.2 Scattering ellipse np, representing the possible positions for the np-th scat-terer related to the CIR model in Fig. 4.1. θnp represents the AoA of the np scatterer. . . 36

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4.3 CIR of a signal emitted by transmitter antenna and received by the na-th

sensor of the antenna array. . . 37 4.4 Ellipse representing the possible positions of the np-th scatterer related to

the CIR model in Fig. 4.3. A two elements ULA is depicted. . . 38 4.5 Approximated CIR of a signal emitted by transmitter antenna and received

by the na-th and na+ 1-th sensors of an antenna array. . . 41

4.6 Examples of the generated CIRs for a 2 antennas receiving array. Ts =

Tsymb/13 . . . . 42

4.7 Scheme of receiver with Low Pass Filter (LPF). . . 43 4.8 Received 4-QAM time signals at the I branch shaped by a Root Raised

Cosine (RRC) filter and received by a proper matched filter. . . 45 4.9 Received 4−QAM signal pdfs, ideal case. (a) C-CP. (b) P-CP. . . 46 4.10 I component of the received 4-QAM time signal. Signal is modulated with

a RRC filter and received by a LPF with rate Ts = Tsymb/6. . . . 47

4.11 Received 4−QAM signal pdfs. Signal is modulated with a RRC filter g and received by a LPF with rate Ts= Tsymb/6. (a) C-CP. (b) P-CP. . . . 48

4.12 Received 4−QAM signal pdfs, Np = 1 multipath case. Line of Sight (LOS)

parameter: α(0)₀ =0deg. Scatterer parameter: α(0)₀ =27deg. (a) C-CP. (b) P-CP. . . 49 4.13 Received 4−QAM signal pdfs, Np = 1 multipath case. LOS parameter:

θ(0)₀ =0deg. Scatterer parameter: θ(0)₁ =−61deg. . . 50 4.14 Received 4−QAM signal pdfs, Np = 1 multipath case. LOS parameter:

θ(0)₀ =30deg. Scatterer parameter: θ(0)₁ =−61deg. . . 51 5.1 Hardware baseband schemes. (a) Transmitter. (b) FPA receiver. (c) TSA

receiver. . . 56 5.2 pdf of the received QAM signal (filtered by an RRC). Left: Cartesian

representation. Right: polar representation. . . 58 5.3 pdf of the received QAM signal (filtered by an RRC and affected by DCO).

Left: Cartesian representation. Right: polar representation. . . 59 5.4 pdf of the received QAM signal (filtered by an RRC and affected by IQU).

Left: Cartesian representation. Right: polar representation. . . 60 5.5 Constellation Statistical Pattern Identification and Overlap (CSP-IDO)

method, no impairments. Differential-Phase of Arrival (PoA) (D-PoA) = −31.3◦_{. (a) Constellations angular histograms. (b) CSP-IDO circular}

correlation. . . 63 5.6 CSP-IDO method, impairment: IQU. D-PoA = −31.3◦. (a) Constellations

angular histograms. (b) CSP-IDO circular correlation. . . 64 5.7 CSP-IDO method, impairment: IQS. D-PoA = −31.3◦. (a) Constellations

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List of Figures vii

5.8 CSP-IDO method, impairment: DCO. PoA = −31.3◦. (a) Constellations

angular histograms. (b) CSP-IDO circular correlation. . . 66

5.9 RMSE for different AoA. Methods A,B and root-MUltiple SIgnal Classifica-tion (MUSIC) (root-MUSIC) algorithm are applied to the FPA, CSP-IDO uses the TSA. (a) Ideal hardware. (b) Impaired hardware. . . 68

5.10 root-mean-square (RMS) error (RMSE) for different AoA. All methods are applied to TSA. (a) Ideal hardware. (b) Impaired hardware. . . 69

5.11 Example of histogram grid with Nang = 16 and Nabs = 6. Each cell has the same surface. . . 71

5.12 Polar representation of C(∆γ(θ0), ρ). Ideal hardware at transmitter side. K = 180◦. . . 74

5.13 Polar representation of C(∆γ(θ0), ρ). Ideal hardware at transmitter side. K = 45◦. . . 75

5.14 Comparison between circular correlations. Ideal hardware at transmitter side. K = 180◦. . . 75

5.15 Comparison between circular correlations. Ideal hardware at transmitter side. K = 45◦. . . 76

5.16 Polar representation of C(∆γ(θ0), ρ). Impaired hardware at the transmitter side. K = 45◦. . . 77

5.17 Comparison between circular correlations. Impaired hardware at the trans-mitter side. K = 45◦_{. . . .} ₇₇

5.18 RMSE(θ, ˜θ) as a function of θ.(a) Ideal transmitter case. (b) Impaired transmitter case. . . 78

5.19 Polar representation of C(∆γ(θ0), ρ). Impaired hardware at the receiver side. K = 45◦. . . 79

5.20 Comparison between circular correlations. Impaired hardware at the re-ceiver side. K = 45◦. . . 79

5.21 RMSE(θ, ˜θ) as a function of θ. Impaired hardware at the transmitter.(a) Ideal receiver case. (b) Impaired receiver case. . . 80

5.22 Polar representation of C(∆γ(θ0), ρ). MP channel, Np0 = 2, τnorm = 2. K = 45◦. . . 81

5.23 Comparison between circular correlations. MP channel, N_p0 = 2, τnorm = 2. K = 45◦. . . 82

5.24 RMSE(θ, ˜θ) as a function of θ in a MP scenario. Impaired hardware at the transmitter. N_p0 = 1. (a) τnorm = 0. (b) τnorm= 1. . . 83

6.1 Experimental set-up. . . 87

6.2 Example of weight reshaping. . . 93

6.3 Driving path for the measurement test. . . 94

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6.5 RMSE for raw estimation and for different PF configurations. . . 96 6.6 Diagram of Confined Area Random Aerial Trajectory Emulator (CARATE)

components for variable φ, example with Nang = 5 . . . 105

6.7 Example of UAV Three-dimensional (3D) trajectory generated with CARATE.106 6.8 Example of UAV angular tracking. Real trajectory and PF and Baseline

Method (BM) estimations are represented. The angular trajectory is traced over a unitary hemisphere. . . 109 6.9 Average Trajectory RMSE (AT-RMSE) for different SNRdB conditions with

dynamic and static σs. . . 110

6.10 AT-RMSE for different normalized 3A-ULA inter-antenna distance Dnorm =

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List of Acronyms

1D Mono-dimensional 2D Bi-dimensional 3A-ULA Three-Axial-ULA 3D-ULA 3D-ULA 3D Three-dimensional A-PSK Amplitude PSK

AoA Angle of Arrival

AT-CRLB Average Trajectory CRLB

AT-RMSE Average Trajectory RMSE

AWGN Additive White Gaussian Noise

BCID 2D CSP-IDO

BM Baseline Method

BND Bivariate Normal Distribution

BS Base Station

C-AWGN Circular-Additive White Gaussian Noise (AWGN)

C-CP Cartesian Complex - pdf

CARATE Confined Area Random Aerial Trajectory Emulator

CIR Channel Impulse Response

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CSP-IDO Constellation Statistical Pattern Identification and Overlap

D-PoA Differential-PoA

D-ToA Differential-ToA

DAC Digital-to-Analog Converter

DCO DC Offset

DC Direct Current

DMM Drift Motion Model

DoA Direction of Arrival

DS Doppler Shift

e.g. exempli gratia (for the sake of an example)

FA-AoA Fully Assisted AoA

FPA Full Parallel Architecture

GL-S Ground Localization Scenario

GNSS Global Navigation Satellite System

GPS Global Positioning System

GSM Global System for Mobile Communications

i.e. id est (that is)

IEEE Institute of Electrical and Electronic Engineers

IQS I-Q Skew

IQU I-Q Unbalance

I In-phase

LOS Line of Sight

LPF Low Pass Filter

LTE Long Term Evolution

MP Multi-path

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List of Acronyms xi

O-AoA Opportunistic AoA

OFDM Orthogonal Frequency Division Multiplexing

P-CP Polar Complex - pdf

PA-AoA Partially Assisted AoA

PC-G Particles Cloud Granularity

PC-W Particles Cloud Width

pdf probability density function

PF Particle Filtering

PL Path Loss

PN Phase Noise

PoA Phase of Arrival

PO Phase Offset

PPA Partially Parallel Architecture

PSAS Particles Swarm Adaptive Scattering

PSK Phase Shift Keying

QAM Quadrature Amplitude Modulation

Q In-quadrature

RFID Radio Frequency (RF) Identification

RF Radio Frequency

RMSE RMS error

RMS root-mean-square

root-MUSIC root-MUSIC RRC Root Raised Cosine

RSSE Received Signal Strength Estimation

RSU Road Side Unit

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SDR Software Defined Radio

SL-S Self Localization Scenario

SMC Sequential Monte Carlo

SNR Signal to Noise Ratio

ToA Time of Arrival

TSA Time Switched Architecture

U-SGM US-CIR based Scattering Geometric Model

UAV Unmanned Aerial Vehicle

ULA Uniform Linear Array

UMTS Universal Mobile Telecommunications System

US-CIR Uniformly Sampled CIR

USRP Universal Software Radio Peripheral

UWB Ultra Wide Band

V2I Vehicle-to-Infrastructure

V2V Vehicle-to-Vehicle

V2X Vehicle-to-Vehicle (V2V) and Vehicle-to-Infrastructure (V2I)

w.r.t. with respect to

WiPLi Lab Wireless and Power Line Laboratory

WSN Wireless Sensor Network

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List of Symbols

Table 1: List of the most commonly used symbols. Symbol Unit Definition

{·}∗ _- _{Complex conjugate operator}

· - Phase operator

E[·] - Expected value operator

[·] (mod a) - Modulo operator with modulus a

AB - Euclidean distance between point A and point B

δ(t) - Dirac delta function in the continuous time domain U (a, b) - Uniform random variable between a and b

N (µ, σ) - Normal random variable with mean µ and standard deviation σ X × Y - Cartesian product between set X and set Y

|Z| - Cardinality of set Z (number of elements) arctan(α) - Inverse function of tan a

arcsin(α) - Inverse function of sin(a) R[·] - Real part operator

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Abstract

This work if focused on the analysis and the development of Angle of Arrival (AoA) radio localization methods. The radio positioning system considered is constituted by a radio source and by a receiving array of antennas.

The positioning algorithms treated in this work are designed to have a passive and opportunistic approach. The opportunistic attribute implies that the radio localization al-gorithms are designed to provide the AoA estimation with nearly-zero information on the transmitted signals. No training sequences or waveforms custom designed for localization are taken into account. The localization is termed passive since there is no collaboration between the transmitter and the receiver during the localization process. Then, the al-gorithms treated in this work are designed to eavesdrop already existing communication signals and to locate their radio source with nearly-zero knowledge of the signal and without the collaboration of the transmitting node.

First of all, AoA radio localization algorithms can be classified in terms of involved signals (narrowband or broadband), antenna array pattern (L-shaped, circular, etc.), sig-nal structure (sinusoidal, training sequences, etc.), Differential-Time of Arrival (ToA) (D-ToA)/Differential-Phase of Arrival (PoA) (D-PoA) and collaborative/non collabora-tive.

Than, the most detrimental effects for radio communications are treated: the Multi-path (MP) channels and the impaired hardware. A geometric model for the MP is analysed and implemented to test the robustness of the proposed methods. The effects of MP on the received signals statistics from the AoA estimation point-of-view are discussed. The hardware impairments for the most common components are introduced and their effects in the AoA estimation process are analysed.

Two novel algorithms that exploits the AoA from signal snapshots acquired sequen-tially with a time division approach are presented. The acquired signals are Quadrature Amplitude Modulation (QAM) waveforms eavesdropped from a pre-existing communica-tion. The proposed methods, namely Constellation Statistical Pattern Identification and Overlap (CSP-IDO) and Bi-dimensional (2D) CSP-IDO (BCID), exploit the probability density functions (pdfs) of the received signals to obtain the D-PoAs. Both CSP-IDO and

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BCID use the statistical pattern of received signals exploiting the transmitter statistical signature. Since the presence of hardware impairments modify the statistical pattern of the received signals, CSP-IDO and BCID are able to exploit it to improve the perfor-mance with respect to (w.r.t.) the ideal case. Since the proposed methods can be used with a switched antenna architecture they are implementable with a reduced hardware contrari-wise to synchronous methods like MUltiple SIgnal Classification (MUSIC) that are not applicable.

Then, two iterative AoA estimation algorithms for the dynamic tracking of moving ra-dio sources are implemented. Statistical methods, namely Particle Filtering (PF), are used to implement the iterative tracking of the AoA from D-PoA measures in two different sce-narios: automotive and Unmanned Aerial Vehicle (UAV). The AoA tracking of an electric car signalling with a Institute of Electrical and Electronic Engineers (IEEE)802.11p-like standard is implemented using a test-bed and real measures elaborated with a the proposed Particles Swarm Adaptive Scattering (PSAS) algorithm. The tracking of a UAV moving in the Three-dimensional (3D) space is investigated emulating the UAV trajectory using the proposed Confined Area Random Aerial Trajectory Emulator (CARATE) algorithm.

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Introduction

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Radio localization techniques such as Angle of Arrival (AoA) algorithms play an impor-tant role in the wider universe of positioning systems, exempli gratia (for the sake of an example) (e.g.), Global Navigation Satellite Systems (GNSSs) [1] applications. The ad-vantage of terrestrial radio localization based methods [2] with respect to (w.r.t.) GNSS is its feasible deployment in environments where satellite visibility is not fully achievable, id est (that is) (i.e.) indoor and canyon like scenarios [3]. Radio localization techiques can be used to implement auto-positioning using known radio anchors or, dually, to remotely locate unknown radio sources [4]. Furthermore, terrestrial radio localization techniques such as AoA do not need the deployment of the extremely expansive and complex satellite constellation infrastructure of GNSS. However, despite the complexity, GNSS provide ad absolute auto-positioning where, in general, radio localization techniques provide a rela-tive localization.

AoA algorithms are dependent on which type of signals the transmitter emits. Several techniques have been developed to locate radio sources emitting specific waveforms, i.e. narrow band signals [5, 6], broad band signals [7] and ad-hoc sequences [8]. Depending on the received signals characteristics different AoA methods are applicable. Further-more, the algorithms can be designed ad-hoc to use certain waveforms and protocols, or they can work opportunistically by intercepting existing signals and requiring the min-imum knowledge on the signal format itself. All local based methods [9], contrarily to distributed ones that rely on a sensor network [10–14], exploit the position of the radio source analysing the differences of its signal impinging on a receiving array of antennas. In case of wideband impulsive signals such as Ultra Wide Band (UWB) transmissions, the parameters that have to be estimated to obtain the AoA are the Time of Arrival (ToA) or the Differential-ToA (D-ToA) [7]. The ToA can be used for ranging measurements [15,16] and for AoA estimations in a passive multiple receiver scenario with a single active source but its calculus needs synchronization between transmitter and receiver. Thus an ad-hoc synchronized system must be settled [17] or a synchronization routine for the receiver

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must be developed [18]. The D-ToAs estimations don’t need synchronization between transmitter and receiver because their computation does not involve ToAs knowledge di-rectly [19]. However, D-ToAs method do not provide didi-rectly a raging estimation. The accuracy achievable by ToA and D-ToA methods is extremely dependent on the time res-olution of the received impulse, and then on its bandwidth, the wider the better. These methods that measure the timing of signals fronts are sensitive to the distance between sensors, the further the better, since received signals are more separated in time [20]. Hence, ToA and D-ToA methods for AoA estimation of impulsive broadband signals are better suited for a distributed sensor localization approach such as Wireless Sensor Net-works (WSNs) [21] or a cellular Base Station (BS) perspective [22]. In case of narrowband signals, such as Radio Frequency (RF) carriers or numeric transmissions, the parameter that has to be estimated to obtain the AoA is the Phase of Arrival (PoA). The PoAs are the phases of the signals received by each antenna. The Differential-PoA (D-PoA) approach for AoA detection imposes the employment of confined arrays w.r.t. ToA meth-ods because of the limited periodic domain of the phase, forcing a local computation of AoA w.r.t. distributed approaches. For the reasons exposed above, a local-based (not distributed) localization approach is achievable using small arrays and a D-PoA approach to exploit localization parameters from narrowband signalling. The aim of this work is to exploit the AoA estimating the D-PoA from narrowband signals such as sine waves and Quadrature Amplitude Modulation (QAM) waves received by an antenna array.

One of the most detrimental effects that affect the radio communication systems is the Multi-path (MP). The MP affect also AoA systems reducing the localization precision. For this reason in Ch. 4 a geometric scattering model for MP is considered to investigate the robustness of the proposed algorithms. A radio-localization system consisting in Na

receiving antennas, 1 transmitting antenna and Npimpairing scatterers is considered [4,9].

The receiving array pattern is arbitrary and can follow the most common L-shape [23] or others geometries, such as circular arrays [24], arbitrary shapes [25] of optimized ones [26, 27]. In Sec. 4.2 is described how to interpret a Uniformly Sampled Channel Impulse Response (CIR) (US-CIR) in terms of geometric position of the scatterers. The relations between the CIRs of different sensors of the same array w.r.t. the same radio source are investigated in Sec. 4.3. The emulation of a geometric based MP channel for a complete array relying on the position of its sensors and one main CIR is discussed in Sec. 4.4. The effects of MP on QAM transmissions and the connection between scatterers positions and the probability density function (pdf) of the received signals is investigated in Sec. 4.5.

Another detrimental cause that impairs the communication systems, comprising AoA systems, is the non ideality of hardware components. The communication systems are composed at the transmitter by a defined set of essential hardware components [28]. These hardware blocks in real scenarios do not have an ideal behaviour and are affected by spe-cific impairments that decrease their performance [29, 30]. The reduction of hardware

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pairments effects on RF communications is achieved on one hand by improving hardware components quality and on the other hand by developing compensation algorithms [31,32]. In Ch. 3 the RF communication systems affected by hardware non idealities are modelled and analysed. The impairing effects on digital communications of a set of impaired hard-ware components is discussed. In particular the effects caused by the impaired transmitter components such as Direct Current (DC) Offset (DCO) (Sec. 3.3), I-Q Unbalance (IQU) (Sec. 3.4), I-Q Skew (IQS) (Sec. 3.5) and Phase Offset (PO) (Sec. 3.6) are investigated. The statistical patterns imposed on the pdfs of received signals by the impaired hardware are interpreted in Ch. 5 such as hardware fingerprints in AoA discovery.

In Ch. 5 two AoA estimation algorithms that are designed to work opportunistically, using random QAM signals, and passively, without the need of calibration or previously agreed protocols are presented. In Sec. 5.1 the Constellation Statistical Pattern Identi-fication and Overlap (CSP-IDO) algorithm is presented [33]. The main features of the proposed technique, namely CSP-IDO, are its reduced hardware needs, its robustness to the hardware impairments of the transmitter, and its fully passive/opportunistic appli-cability. The CSP-IDO method, illustrated in Sec. 5.1.4, is based on the analysis of the pdfs of successive signal snapshots taken from the antennas (asynchronous approach). Contrariwise, other AoA methods, such as beamforming [34,35] and root-MUltiple SIgnal Classification (MUSIC) (root-MUSIC) [36], have been conceived to synchronously (in par-allel) acquire signals from the antenna elements (synchronous approach). In Sec. 5.2 an extension of CSP-IDO is presented. The CSP-IDO method exploits the statistical phase pattern of the received signals to estimate the D-PoA. Instead, the proposed CSP-IDO ex-tension, namely Bi-dimensional (2D) CSP-IDO (BCID), exploits the D-PoA, from the full bi-dimensional statistical pattern of received signals showing more robustness w.r.t. the impairments of the receiver. Furthermore, both CSP-IDO and BCID are able to improve their performance exploiting the transmitter impaired hardware signature introduced in Ch. 3. Since the use of the proposed methods exploits the received signals pdfs, their application is feasible with any type on numerically modulated signal, such as QAM. The performance has been evaluated also in scenarios where the estimation process is affected by MP and impaired by hardware at the receiver showing enough robustness. Proposed techniques thanks to their passive/opportunistic approach to AoA localization and thanks to the limited hardware usage are suited to be applied in a eavesdropping scenario with low-end hardware.

Differently to the static methods proposed in Ch. 5 in Ch. 6 are discussed, imple-mented and tested two possible applications for dynamic AoA tracking using Particle Filtering (PF) algorithms. Sec. 6.1 is focused on the application of AoA estimation in the automotive scenario. A vehicular communication network most likely based on Institute of Electrical and Electronic Engineers (IEEE) 802.11p [37] will become soon a reality. This will enable the establishment of ad-hoc car networks for the diffusion and gathering

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of sensor information and the implementation of a plethora of new services [38]. Among all possible new applications, the most important ones are probably those that exploit localization information, i.e., context aware services. In this respect, Global Position-ing System (GPS) positionPosition-ing plays an important role in the full development of this ecosystem of services. However, the usage of other localization technologies is relevant in situations where GPS does not fulfil the requirements, e.g., in terms of precision, re-sponse time, and coverage. The usage of Road Side Units (RSUs)) that detect position information from vehicles is interesting for instance to offer a traffic control monitoring service for safety [39] or vehicle flows analysis and management [40], or it can be an enabling service for consumer applications like driver assistance and in the emerging tech-nology of self-driving cars. Therefore, a different type of localization method that exploits an existing vehicular communication network infrastructure (and in particular the IEEE 802.11p network) in an “opportunistic” way is discussed. The proposed method tries to obtain the vehicles position, in a certain area, by listening to Vehicle-to-Vehicle (V2V)-Vehicle-to-Infrastructure (V2I) communication signals using an RSU. Such an approach can avoid the use of GPS or complement it, provide more accuracy and reliability in certain scenarios. Essentially, this approach is host-based, i.e., it is made directly by the RSU node. This AoA estimation approach can be challenging because of hardware impairments (as phase noise) and multipath propagation [41]. AoA estimation can be done with subspace methods as the MUSIC algorithm [42] which detect multiple emitters and compensate, in part, multipath effects. A simple AoA phase differential approach is considered. Then, the AoA estimates are refined using a statistical method based on PF [43]. Particle filtering was proposed originally for iteratively estimate the hidden state of a dynamic system approximating its continuous pdf with a weighted set of M discrete samples [44]. The experimental test bed visible in Fig. 6.1 has been deployed to evaluate algorithm performance.

Sec. 6.2 is focused on the application the AoA estimation in a Unmanned Aerial Vehicle (UAV) localization scenario. UAVs are attracting considerable attention since they can be used for a number of consumer, industrial and military applications ranging, for instance, from sport video making to environmental monitoring and parcel delivery [45,46]. A key component is the technology that allows to locate and navigate the UAVs. Presently, GNSS and inertial sensors are used to provide information on position, speed and direction of movement. Reliable localization is very important also in view of new regulations that aim at better controlling the use and the status of the UAVs for higher safety and security [47]. Furthermore recently UAVs technology has started to be under the spotlight of police audits because of possible security threats [48].In Sec. 6.2, a radio localization approach is considered and it is based on azimuth and elevation positioning using a transmitting source as a reference. Azimuth and elevation are determined by processing with PF the signals that impinge on a Three-Axial-Uniform Linear Array (ULA) (3A-ULA). The

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5

3A-ULA can be mounted either on a ground base station or on the UAVs. In the first case, namely Ground Localization Scenario (GL-S), the base station passively eavesdrops the signals emitted by the UAVs to determine their angular coordinates. In the latter case, namely Self Localization Scenario (SL-S), the ground node acts as a radio anchor allowing UAVs self localization. The system can be used in a standalone way or to complement existing GNSS or inertial sensors employing data fusion techniques [49].

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AoA Estimation Techniques

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Radio localization techniques such as Angle of Arrival (AoA) algorithms play an impor-tant role in the wider universe of positioning systems, exempli gratia (for the sake of an example) (e.g.), Global Navigation Satellite Systems (GNSSs) [1] applications. The ad-vantage of terrestrial radio localization based methods [2] with respect to (w.r.t.) GNSS is its feasible deployment in environments where satellite visibility is not fully achievable, id est (that is) (i.e.) indoor and canyon like scenarios [3]. Radio localization techiques can be used to implement auto-positioning using known radio anchors or, dually, to remotely locate unknown radio sources [4]. Furthermore, terrestrial radio localization techniques such as AoA do not need the deployment of the extremely expansive and complex satellite constellation infrastructure of GNSS. However, despite the complexity, GNSS provide ad absolute auto-positioning where, in general, radio localization techniques provide a rela-tive localization.

Introduction

The aim of AoA techniques (called also Direction of Arrival (DoA)) [2, 4, 9] is to estimate the angular position φ of a radio source w.r.t. a receiver Fig. 2.1. Angular localization of radio sources is used in a wide set of scenarios such as Unmanned Aerial Vehicle (UAV) navigation and positioning [50], Radio Frequency (RF) Identification (RFID) tags monitoring [51] and wildlife monitoring [52]. The AoA receiver is equipped with an antenna array. The AoA estimations are made elaborating the signals impinging on each sensor of the array. The AoA methods can be used jointly with data fusion techniques [49, 53] using ranging sensors [54] to provide the full localization of the emitter. Full Three-dimensional (3D) localization can also be reached using jointly AoA estimates of several receivers in different positions [55].

Changing the point of view to a self localization perspective, AoA estimation, if applied to a scenario with radio emitting anchors with known position or pattern, allows the

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Figure 2.1: AoA estimation array system.

receiver Bi-dimensional (2D) or 3D self positioning [6].

AoA algorithms are dependent on which type of signals the transmitter emits. Several techniques have been developed to locate radio sources emitting specific waveforms, i.e. narrow band signals [5, 56], wide band signals [7, 22, 57, 58] and ad-hoc training sequences [8, 59]. Furthermore, the algorithm can be designed ad-hoc to use certain predetermined waveforms or protocols [60] or it can work opportunistically by intercepting existing signals and requiring minimum knowledge on the signal format itself Ch. 5.

In the following Sections features and techniques of AoA estimation methods applied to different scenarios are presented.

Opportunistic and Assisted Techniques

One important feature of AoA techniques is how much the localization is coordinated and concerted between the involved nodes.

In the most complete scenario, herein named Fully Assisted AoA (FA-AoA) scenario, the transmitter and the receiver are connected with an ad-hoc service channel to allow localization [10, 61–63]. Through this connection the receiver instructs the transmitter and sends signals specification and scheduling times, allowing a fully assisted localization approach. The evident quality of this technique is the flexibility on transmitted wave-forms and its versatility for on-demand-like positioning applications. The drawback is the complexity caused by the control channel and the high level protocols management, that implies the creation of an ad-hoc communication protocol and more complex units.

Non assisted methods, namely Opportunistic AoA (O-AoA), have a totally passive approach to localization, without the collaboration or the knowledge of the transmitter. In the O-AoA the receiver exploits the position of the receiver from generalized RF signals.

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2.3 - Received Signals Types 9

The receiver has only a low level knowledge about the transmitter, for example the the modulation scheme, such as Quadrature Amplitude Modulation (QAM) [33], the central frequency or the existence on training sequences such as orthogonal signatures like in Long Term Evolution (LTE) [64,65],Universal Mobile Telecommunications System (UMTS) [66, 67] or channel estimation sequences [68] like in Global System for Mobile Communications (GSM) [69].

Partially Assisted AoA (PA-AoA) methods have hybrid proprieties w.r.t. FA-AoA and O-AoA techniques [70]. PA-AoA does not involve communication between transmitter and receiver but uses a pre-agreed algorithm or known signal. In PA-AoA methods the receivers can exploit the position of transmitter through previously agreed signals, sent for example in planned times or intervals.

The collaborative multi receiver schemes designed to provide 2D or 3D localization mentioned in Sec. 2.1 introduce the further complexity typical of Wireless Sensor Networks (WSNs) [21]. In fact, to apply data fusion or in general data aggregation in a WSN scenario several service channel must be deployed because of the intrinsic necessity to spread/aggregate the information across the distributed architecture of sensors.

The aim of this work is to exploit AoA from radio signals opportunistically i.e. with-out the need of coordination among nodes. Such techniques, implemented by non-collaborative nodes, in general achieve less precision that ad-hoc methods but can be applied in a broader set of scenarios and are more flexible. Then, the algorithms treated in this work are designed to eavesdrop already existing communication signals and to locate their radio source with nearly-zero knowledge of the signal and without the collab-oration of the transmitting node.

Received Signals Types

A central characteristic that distinguish AoA methods is the type of signals involved in the localization techniques. Depending on the received signals different AoA methods are applicable. All local based methods, contrarily to distributed ones such as WSN, exploit the position of the radio source analysing the differences of its signals impinging on a receiving array of antennas.

In case of wideband impulsive signals with sharp patterns in time, the parameter that has to be estimated to obtain the AoA is the Time of Arrival (ToA) or secondary the Differential-ToA (D-ToA) [7, 71]. The ToA is the time that the sent signal takes to go from the transmitter antenna to the receiver antenna. The ToA can be used for ranging measurements and for AoA estimations in a multiple receiver scenario. The ToA estimation needs synchronization between transmitter and receiver to be correctly computed. Thus an ad-hoc synchronized system must be settled [17] or a synchronization routine for the receiver must be developed [18]. The D-ToAs are the difference of arrival

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times of the emitted impulse between the couples of antenna sensors at the receiver. The D-ToAs doesn’t need synchronization between transmitter and receiver because their computation doesn’t involve ToAs knowledge directly [19].

The accuracy achievable by ToA and D-ToA is extremely dependent on the time du-ration of the impulse and then to its bandwidth. Using a D-ToA approach with wideband signals for DoA estimation the precision increases with the distance between array ele-ments, since received signals are more separated in time [14, 20]. Hence, ToA and D-ToA methods for AoA estimation of impulsive broadband signals are better suited for a dis-tributed sensor localization approach such as WSNs [21] or a cellular Base Station (BS) perspective [22].

In case of narrowband signals, such as RF carriers or QAM transmissions, the param-eter that has to be estimated to obtain the AoA is the Phase of Arrival (PoA). The PoAs are the phases of the signals received by each antenna sensor. In particular, it is exploited the Differential-PoAs (D-PoAs) that is the difference between the phases of the impinging waveforms detected by each antenna. As discussed in Sec. 2.4, because of the periodic support of the D-PoA, namely [−π, pi[, it is necessary to force an upper bound in the inter antenna distance of the array to uniquely detect the phase [20]. The D-PoA approach for AoA detection allows/imposes the employment of more confined arrays w.r.t. D-ToA methods, forcing a local computation of AoA w.r.t. the distributed approaches.

For the reasons exposed above, a local-based (not distributed) localization approach is achievable using small arrays and a D-PoA approach to exploit localization parameters from narrowband signalling. The aim of this work is to exploit the AoA from narrowband signals such as sine waves or QAM waves.

Phase of Arrival Methods

As discussed in Sec. 2.2 and Sec. 2.3 the purpose of this work is to opportunistically esti-mate the AoA of a transmitter exploiting its emitted narrowband signals. The standard lo-calization scenario that will be considered in the following is visible in Fig. 2.1. It is consti-tuted, at the receiver side, by an array of Naantennas each one positioned in the 3D space

at the coordinates [x(i), y(i), z(i)]. The transmitter is positioned in [x(T X), y(T X), z(T X)]. Sig-nals emitted from transmitter are considered impinging receiver antenna array as plane waves [72], for this reason its distance from receiver array must be substantially greater than array size w.r.t. carrier wavelength λ0. Considering a numerical narrowband RF

transmission the demodulated signal sampled at rate 1/Tsymb, is

s(i)_n = Anejψ

(i)

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2.4 - Phase of Arrival Methods 11

where the index i identifies the antenna of the array and n represents the time instant

nTsymb. The Additive White Gaussian Noise (AWGN) is represented by the term w(i)n .

The numerical symbols transmitted by the numerical modulation such as Amplitude Phase Shift Keying (PSK) (A-PSK) or QAM are defined by the parameter An = |an|ejξn ∈ A

that is considered a uniform random variable inside its limited set of values A. Tsymb

is the symbol period. The parameter ψ(i) represents the PoA of the transmitted signal impinging to the i-th antenna, in particular

ψ(i) = 2πf0τ(i) (2.2)

where τ(i) _{= D}(i)_/c

0 is the i-th ToA. The distance between the transmitting antenna

and the i-th receiving sensor of the antenna array is D(i) and f0 is the carrier frequency

of the RF numerical transmission. The constant c0 represents the speed of light an its

value is 299792458m/s. Since the parameter used for the AoA estimation θ is the D-PoA

δψ(i) _{= ψ}(i+1)_{− ψ}(i)_{, its calculus is related to the inter-antenna distance d}(i)_:

δψ(i) =hψ(i+1)− ψ(i)i (mod 2π) =h2πf0(τ(i+1)− τ(i)) i (mod 2π) = " 2πd (i) λ0 sinθ + δθ(i) # (mod 2π) (2.3)

where δτ(i) _{is the D-ToA for the antenna i and the operator [·] (mod 2π) represents the}

modulo operator with interval 2π . The parameter δθ(i) _{is a phase adjustment factor that}

expresses the physical inclination of the i-th and the i + 1-th couple of antennas w.r.t. the y axis. The support of the phase is limited and periodic, for this reason to uniquely decode the D-PoA for every possible AoA θ between −π and π it must be that

|2πd

(i)

λ0

sinθ + δθ(i)| ≤ π ∀(θ + δθ(i)_{) ∈ [−π/2, π/2) =⇒ d}(i) _{≤ λ}

0/2 (2.4)

where λ0 = c0/f0 is the carrier frequency wavelength. As discussed in [20] the constrain

in (2.4) limits the use of D-PoA methods to small sized antenna arrays. Considering the scenario of (2.1) depicted in Fig. 2.1 the D-PoA δψ(i) _{can be calculated as}

δ ˜ψ(i) = s(i+1) n − s(i)n (2.5) where Ehδ ˜ψ(i)i= Eh Anejψ (i+1) + w(i+1) n − Anejψ (i) + w(i) n i , = Anejψ (i+1) − Anejψ (i) ,

= ψ(i+1)− ψ(i) _{= δψ}(i)_.

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Figure 2.2: Arrays for AoA estimation. L array (left). X array (right).

and where δ ˜ψ(i) _{is the estimation of the real D-PoA δψ}(i) _{and the operator E[·]}

repre-sents the expected value. The noise component in 2.1 does not affect 2.6 because of the expectation operation. The value of δ ˜ψ(i) _{is then used to estimate with ˜}_θ(i) _{the AoA θ:}

˜ θ(i) = arcsin −δ ˜ψ (i) K(i) ! − δθ(i) (2.7)

where, as depicted in Fig. 2.1, K(i) = 2πd(i)/λ0 expresses the inter element distance i

normalized to the wavelength λ0, in angles. Each antenna pair of the array produces an

AoA estimation ˜θ(i)_{, all estimations can be averaged in a single result. Otherwise, (2.7)}

can be applied to an average D-PoA between the Npairs available antenna pairs of the

array δ ˜ψ =PNpairs

i=1 δ ˜ψ(i)/Npairs.

Antenna Array Patterns

The array of antennas used for AoA estimation is a fundamental part of receiver hardware since the received signals rely on the sensors position and geometry. The position of antennas in the array influences the received signals, in particular their time and phase shifts, as explained in (2.3). Different array geometries rely on different parameters for localization algorithms. The most common array configurations are Uniform Linear Array (ULA) and L-shaped arrays [23] for Mono-dimensional (1D) and 2D angular positioning, respectively (Fig. 2.2). Both systems described in Fig. 2.2 are composed of three branches each one composed by a ULA lying in a different axis. The ULAs are arrays composed by equispaced sensors lying on the same line, for this reason the schemes in Fig. 2.2 will be herein considered as 3D-ULAs (3D-ULAs). Usually contiguous antennas of the same branch have the same inter-element distance. As described in (2.4) inter-antenna distance

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2.5 - Antenna Array Patterns 13

is crucial for D-PoA estimators since it influences the estimation process. If a maximum range is fixed for the AoA estimation (|θ| < θmax), the maximum value for the inter

element distance d is d ≤ λ0 2 1 sin (θmax) , (2.8)

where for the sake of simplicity the array is considered parallel to the y axis: δθ=0. On the other hand if the carrier wavelength λ0 and the inter-element distance d are fixed, the

range of the AoAs θ that can be correctly detected |θ| < θmax is limited by

θmax= arcsin

λ0

2d !

, (2.9)

where, again, for simplicity the array is considered parallel to the y axis: δθ=0. Limitation expressed in (2.8) and (2.9) can be mitigated using complex arrays that lead to several AoA estimations ˜θ(i).

The arrays depicted in Fig. 2.2, exploit both azimuth and elevation coordinates of a RF source. In particular the L-shaped 3D-ULA in Fig. 2.2 is constituted, for each one of the 3 branches, by Na antennas. Each branch is labelled with a ∈ x, y, z to indicate along

which one of the axes it is displaced. An antenna of the same branch a is indexed with

i ∈ [1, 2, . . . , Na] to indicate its position along the branch. Thus, the coordinates of the

antennas can be written as

x(a,i) = (i − 1)dδxa,

y(a,i) = (i − 1)dδya,

z(a,i) = (i − 1)dδza,

(2.10)

where δij is the Kronecker delta that is 1 for i = j and 0 otherwise and d is the constant

distance between antennas. The notation of received signal

s(a,i)_n = Anejψ

(a,i)

n _{+ w}(a,i)

n , (2.11)

is compliant to (2.1) for all branches a. The D-PoAs for the branch a are defined as ˆ

ψ(a)

n = ψ(a,2i−1)n − ψ(a,2i)n ∀i ∈ [1, 2, . . . , Na/2]. In [73] a technique to estimate ˆψn(a) is

described. Applying this technique for the model considered allows to exploit the D-PoAs of the branches from the signal model introduced in (2.11). ˆψ(a)

n are estimated as u(a)n ,

where · stands for the phase operator and where:

u(a)_n = 2 Na Na/2 X i=1 s(a,2i−1)_n s(a,2i)_n ∗, (2.12)

where an average over the Na/2 distinct antenna pairs is performed to mitigate the AWGN

effect. Using u(a)

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with ˜θn and ˜φn as following: ˜ θn= arctan q ( u(x) n )2 + ( u(y)n )2, u(z)n , ˜ φn = arctan u(y)_n , u(x) n , (2.13)

where arctan(·, ·) is the arctangent function extended to the [0, 2π) domain.

In this work ULAs are used for AoA estimation however several array geometries are treated in literature, such as circular arrays [24] or more generic arrays [25]. Different tech-niques have been proposed to optimized arrays geometries in different scenarios, mainly minimizing the array Cramér-Rao Lower Bound (CRLB) w.r.t. AoA error [26, 27].

Hardware Architectures

The elaboration of radio signals impinging on antenna sensors of a pre-determined array for AoA exploitation can be performed using different receiving hardware schemes. Re-ceiving architectures differ mainly on how much hardware is shared among each sensor branch.

Full Parallel Architecture (FPA)

The more complete solution is depicted for the sake of the example in Fig. 2.3. It pro-vides Na different receiving complex branches, each one comprising both In-phase (I) and

In-quadrature (Q) channels, it is herein named FPA. FPA provides two completely inde-pendent complex receiving branches. Each antenna branch is provided by an indeinde-pendent oscillator as reference for the RF down-converting process. In case of impairing hardware, discussed in Ch. 3), each branch will provide completely independent received signals modifications. The most impairing effect is the asymmetric Phase Offset (PO), the phase misalignment between oscillators. For the sake of the example, this receiving scheme is used in [74] for AoA estimation and for the characterization of hardware impairments.

Partially Parallel Architecture (PPA)

The PPA architecture scheme partially shares hardware components, it depicted for the sake of the example in Fig. 2.4. This scheme provides Na different receiving complex

branches, each one comprising both I and Q channels, it is herein named PPA. The PPA provides two completely independent complex receiving branches except for the oscillator, that is in common between the branches. The common oscillator feeds all the mixers trough a splitter circuit. In case of impairing hardware, discussed in Ch. 3), each branch will provide different Q Unbalances (IQUs), Direct Current (DC) Offsets (DCOs) and I-Q Skews (II-QSs). Branches will experience the same PO caused by the common oscillator.

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2.6 - Hardware Architectures 15

Figure 2.3: FPA receiving scheme, Na = 2.

However, PO asymmetries can be verified if circuits that connect the oscillator splitter to the different mixers are affected by different delays. The difference between POs that affects the system is 2πf0(l(2)− l(1))/c0, where l(1) and l(2) are the circuits lengths of the

two connections that goes from the first mixer to the splitter and from the second mixer to the splitter, respectively.

Time Switched Architecture (TSA)

The Time Switched Architecture (TSA) architecture shares more components w.r.t. 2.6.1 and 2.6.2 and is treated in Ch. 5 and depicted for the sake of the example in Fig. 2.5. It provides 1 receiving branch, that is shared among all receiving antennas. Antennas are then time duplexed in the shared receiving architecture, namely TSA. Antenna branches share, in the case of hardware impairments, the same IQU, DCO, PO and IQS. The TSA provides also different PO because the oscillator is common for all antennas. However, PO asymmetries can be verified if connections that connect the antenna switch to the different antennas are affected by different delays. The difference between POs that affects the system is 2πf0(L(2)− L(1))/c0, where L(1) and L(2) are the circuits lengths of

the two connections that goes from the first antenna to the switch and from the second antenna to the switch, respectively. This type of architecture is used in Ch. 5 and [33] for AoA purposes exploiting its impaired hardware fingerprint.

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Figure 2.4: PPA receiving scheme, Na = 2.

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2.7 - Error Evaluation 17

Error Evaluation

The AoA estimation algorithms performance are evaluated computing the root-mean-square (RMS) error (RMSE) parameter. This value is defined as

θRMSE(θ) =

s

PN

n=1(θ − θest)2)

N (2.14)

where θ is the real AoA, θest is the estimated AoA and N is the number of estimations

processed by the algorithm. The RMSE, assuming an unbiased estimation, is the standard deviation of the estimation error θ − θest. To fix the ideas in a 1D example, the value

θRMSE can be used to generate an angular uncertainty interval around the real value θ:

B(θ) = [θ−θRMSE, θ+θRMSE]. From the Čebyšëv’s inequality, about the 68% of estimations

for θ fall inside the uncertainty interval B(θ) if the error id Gaussian. Such error interval

B(θ) graphically shows how wide is the estimation error since it contains the 68% of the

iterated estimations.

Considering a 2D scenario where both azimuthal AoA φ and elevation AoA θ are jointly estimated, an error evaluation parameter is herein proposed. A standard approach is to calculate both RMSEs for azimuthal and elevation coordinates: θRMSE(θ, φ) and

θRMSE(θ, φ). Both RMSEs are dependent by φ and θ. However, in this 2D angular

scenario θRMSE(θ, φ) and φRMSE(θ, φ) do not give a correct error perception like in the

previous 1D scenario. In fact, if for the sake of the example we consider an estimation algorithm with φRMSE = 5◦, the same RMSE value in θ = 10◦ will lead to a lower position

knowledge w.r.t. the same RMSE in θ = 85◦, see Fig. 2.6. This phenomenon is due to the definition of the spherical coordinates system that lead to smaller circles of latitude near the poles w.r.t. the equator.

In order to have a better angular error estimation parameter, a new metric is proposed, the Solid Angle RMSE (SARS). The SARS ΩRMSE(θ, φ) is defined as the solid angle

occupied by the uncertainty surface B(θ, φ), that is lying on a unitary sphere. B(θ, φ) is delimited along the elevation coordinate by the two circles of latitude located in θ −

θRMSE(θ, φ) and θ + θRMSE(θ, φ). The surface B(θ, φ) is bounded along the azimuthal

coordinate by the two meridians positioned in φ − φRMSE(θ, φ) and θ + θRMSE(θ, φ). The

considered surface is a spherical rectangle [75] centred in [θ, φ], its angular area can be calculated as ΩRMSE(θ, φ) = 1 πφRMSE(θ, φ) sin θRMSE(θ, φ) 2 ! sin(θ) . (2.15) ΩRMSE(θ, φ) is an a-dimensional parameter that express the angular area of B(θ, φ) in

steradians normalized by the angular area of the hemisphere, that is 2π [sr]. In Fig. 2.6 are depicted on a unit hemisphere 5 examples of spherical rectangles B(θ, φ) generated with the same RMSEs, namely θRMSE = φRMSE = 20◦, but in different coordinates. In

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Figure 2.6: Example of 2D angular uncertainty surfaces B generated by the same 1D angular uncertainties δφ = δθ = 20◦ and leading different Ω values.

Fig. 2.6 is evident how the same RMSEs generate different uncertainty surfaces at different coordinates

Conclusions

In this Sec. an overview of AoA techniques for radio sources localization has been car-ried out. In particular different scenarios have been introduced, such as AoA collabo-rative/opportunistic approaches (Sec. 2.2), received signals types (Sec. 2.3), estimation techniques (Sec. 2.4), receiving antenna arrays (Sec. 2.5) and hardware architectures (Sec. 2.6). Finally a novel parameter, namely SARS, is proposed to evaluate the per-formance of 2D AoA estimation algorithms. Then, the algorithms treated in the following (Sec. 6 and Sec. 5) will be designed to eavesdrop already existing communication signals and to locate their radio source with nearly-zero knowledge of the signal and without the collaboration of the transmitting node.

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Hardware Impairments in

AoA Estimation

3

In this Ch. the RF communication systems affected by hardware non idealities are mod-elled and analysed (Sec. 3.2). The impairing effects on digital communications of a set of impaired hardware components is discussed. In particular the transmitter components effects such as DCO (Sec. 3.3), IQU (Sec. 3.4), IQS (Sec. 3.5) and PO (Sec. 3.6) are investigated.

Introduction

Every communication system is, in general, composed at the transmitter by a defined set of essential hardware components [28]. These hardware blocks in real scenarios do not have an ideal behaviour and are affected by specific impairments that decrease their per-formance [29, 30]. The reduction of hardware impairments effects on RF communications is achieved on one hand by improving hardware components characteristics and receiving architectures and on the other hand by developing compensation algorithms [31, 32].

Hardware System Models

Considering, for the sake of the example, the zero intermediate frequency (zero-IF) [76,77] depicted in Fig. 3.1, the hardware modules that influence transmitted symbols are:

• the Digital-to-Analog Converter (DAC) for the digital-to-analogic signal conversion. • the transmission filter that can be performed digitally before the DAC.

• the mixer for the frequency up-conversion,

• the oscillator that generates the sinusoidal signal for the frequency up-conversion, • the 90◦ _{phase shifter for orthogonal bases generation needed in I and Q branches,}

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Figure 3.1: zero-IF transmitter.

Figure 3.2: zero-IF receiver.

In the following of this Ch. the impaired hardware effects are treated and compared to the ideal case. The effects of hardware impairments on numerical modulations such as QAM and A-PSK [78,79] are treated. The transmitter architecture considered is depicted in Fig. 3.1 as a zero-IF. The receiver architecture considered is depicted in Fig. 3.2 as a zero-IF. The RF signal impinging at the receiver’s antenna z(RF )_{(t) is generated}

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3.2 - Hardware System Models 21

signal z(RF )_{(t) is then down-converted by receiver branches generating}

yn= y(I)n + jy

(Q)

n , (3.1)

where y(I)

n and yn(Q)are the signals elaborated by the I and Q branches respectively. In the

ideal case where impairments are not considered and where receiving filter is synchronized and matched with the transmitter’s one

yn = an+ wn (3.2)

where symbols an are the elements of a unitary energy M -sized numerical

constella-tion . The parameter wn ∼ N (0, σw) is the sampled additive white Circular-AWGN

(C-AWGN) with zero mean and standard deviation σw. In Fig. 3.3 are depicted the ideal

bi-dimensional probability density functions (pdfs) of the received complex signal yn that

express a QAM modulation, after all the receiving chain. The Fig. 3.3.(a) depicts the Cartesian Complex - pdf (C-CP) of yn that jointly depicts the pdfs of of R[yn] and I[yn].

The operators R[·] and I[·] represent the real part and the imaginary part operators, respectively. In the ideal case, considered in this Sec. , the joint pdf of the real and imaginary parts of yn, namely yn(I) and y(Q)n , is

f (yn) = M X m=1 P [an= a(m)] · fN2  y_n,   R(a(m)₎ I(a(m)₎  , σ2_wI₂   , (3.3)

where the matrix I2 is the 2 × 2 identity matrix. The symbol a(m) represents the m-th

element of an M sized numerical constellation and its occurrence probability is P [an =

a(m)]. The function fN2 in (3.3) represents the pdf of the Bivariate Normal Distribution

(BND) that is defined as fN2(y, ¯µ, Σ) = 1 2π|Σ|1/2e 1 2(¯y−¯µ) T_Σ−1_(¯_y−¯_µ) , ¯ y =hR(y) I(y)iT , ¯ µ =hR(µ) I(µ)iT , Σ =   σ2R ρσRσI ρσIσR σI2   , (3.4)

where the vector ¯y comprises the real and the imaginary parts of y, and ¯µ is the mean

vector. The parameter Σ is the covariance matrix of the real and imaginary parts. The variables σR and σI are the standard deviations of R(y) and I(y), respectively. The

parameter ρ is the correlation coefficient between R(y) and I(y).

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the pdfs (3.3) of |yn| and ∠yn. The operators | · | and ∠· represent the absolute value and

the phase operator, respectively. Equivalently the Fig. 3.4 shows respectively in (a) and (b) the P-CP and C-CP of yn in (3.3) expressing an A-PSK modulation. The analytical

Figure 3.3: Received 16−QAM signal pdfs, ideal case. (a) C-CP. (b) P-CP. expression in (3.3) supported by Fig. 3.3.(a) and Fig. 3.4.(b)show that the pdfs of the received signal are constituted by M BNDs translated into the complex coordinates of transmitted symbols, where M is the cardinality of the constellation. Both patterns of (3.3) generated by QAM and A-PSK show regular geometric behaviours, along x and y in the Cartesian representations,Fig. 3.3.(a) and Fig. 3.4.(a), and along the phase axis in the polar representations Fig. 3.3.(b) and Fig. 3.4.(b). In particular the depicted 16-QAM C-CP exhibits a√M periods of symmetry for both x and y axis that are expressed in the

P-CP with 4 periods of symmetry along the phase axis. The depicted 12-4-A-PSK pdfs exhibits in both a C-CP and P-CP 4 periods of symmetry along the phase axis. In the following of the Ch. the varying behaviour of this patterns will be analysed considering an impaired transmitter and an ideal receiver.

DC Offset (DCO)

The DC Offset (DCO) detrimental effect [31, 80] is caused by the non-ideal behaviour of the the DAC. The DAC [76] purpose as depicted in Fig. 3.1 is to change the transmitted

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3.3 - DC Offset (DCO) 23

Figure 3.4: Received 8-4-A-PSK signal pdfs, ideal case. (a) C-CP. (b) P-CP.

symbols digital domain that is Z(Tsymb) to the analogic one R. Typically inside a

trans-mitter architecture are present two DACs, see Fig. 3.1, or a double input - double output DAC to convert both I and Q channels is present. The DAC is followed by a proper transmission filter g. The DACs I and Q input channels are respectively a(I)

n and a(Q)n , the

real and imaginary parts of the transmitted symbols, respectively. Then, I and Q ideal output channels are respectively ˆx(I)

n and ˆx(Q)n , where:

ˆ

x(I)₍ t) = x(I)_n ∗ g(t) , ˆ

x(Q)₍ t) = x(I)_n ∗ g(t) , (3.5) where the transmitted symbols are shaped with the transmitting filter g.

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DCO Hardware Causes

The input discrete signals of the DAC stage, namely a(I)_n and a(Q)_n don’t have, in general, DC components: lim N →∞ N X n=0 a(I)_n = 0 , (3.6) lim N →∞ N X n=0 a(Q)_n = 0 , (3.7)

so that neither the continuous components ˆx(I)₍ t) and ˆx(Q)₍ t) have biases. The hardware

realization of the DACs because of non ideal characteristics of electronic components [81] can generate a non zero bias for both real output channels ˆx(I)_DCO(t) and ˆx(Q)_DCO(t) w.r.t. ideal ones, ˆx(I)_{(t) and ˆ}_x(Q)_{(t), respectively:}

ˆ

x(I)_DCO(t) = ˆx(I)(t) + δ_DCO(I) ,

ˆ

x(Q)_DCO(t) = ˆx(Q)(t) + δ(Q)_DCO, (3.8)

where respectively δ_DCO(I) and δ_DCO(Q) are the DC biases introduced by hardware imperfec-tions by the DAC to I and Q channels, respectively.

DCO Effects on Constellations

The biases introduced by the impaired DCO [77] generate the following pdf at the receiver side for yDCO,n= y

(I) DCO,n+ jy (Q) DCO,n fDCO(yDCO,n) = 1 M M X m=1 fN2  y_DCO,n,   R(a(m)_{+ δ} DCO) I(a(m)_{+ δ} DCO)  , σ_wI₂   , (3.9) where δDCO = δ (I) DCO + jδ (Q)

DCO is the aggregated offset introduced to I and Q channels.

The DCO affects the pdf translating its domain. The DCO impaired pdf expressed in (3.9) is depicted in Fig. 3.5 and Fig. 3.6 for a 16-QAM and a 12-4-A-PSK numerical con-stellation respectively. Both pdfs patterns for (3.9) generated by QAM and A-PSK show different geometric behaviours w.r.t. the ideal ones depicted in 3.3 and 3.4, respectively. In particular, because of the bi-dimensional translation of the pdf in the Cartesian space of [δ_DCO(I) , δ_DCO(Q) ] and in the polar space of [|δDCO|, ∠δDCO] the symmetries of the ideal case

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3.3 - DC Offset (DCO) 25

Figure 3.5: Received 16-QAM signal pdfs showing DCO effects. (a) C-CP. (b) P-CP.

Opportunistic Angle of Arrival Estimation in Impaired Scenarios

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UNIVERSITÀ DEGLI STUDI DI UDINE

Dipartimento di Ingegneria Elettrica, Gestionale e Meccanica

Corso di Dottorato in Ingegneria Industriale e dell’Informazione

Ciclo XXIX

Tesi di Dottorato di Ricerca

OPPORTUNISTIC ANGLE OF ARRIVAL

ESTIMATION IN IMPAIRED SCENARIOS

Dottorando:

ANDREA PAPAIZ

Relatore:

Prof. ANDREA M. TONELLO

ANNO ACCADEMICO

2016/2017

To <insert your name>,

for your outstanding <insert your quality>.

Ringraziamenti

Contents

List of Figures

List of Acronyms

List of Symbols

Abstract

Introduction

1

AoA Estimation Techniques

2

Introduction

Opportunistic and Assisted Techniques

Received Signals Types

Phase of Arrival Methods

Antenna Array Patterns

Hardware Architectures

Full Parallel Architecture (FPA)

Partially Parallel Architecture (PPA)

Time Switched Architecture (TSA)

Error Evaluation

Conclusions

Hardware Impairments in

AoA Estimation

3

Introduction

Hardware System Models

DC Offset (DCO)

DCO Hardware Causes

DCO Effects on Constellations